The complete (continuous) frequency response is defined using the DTFT (see
§B.1), i.e.,

where the summation limits are truncated to
because
is zero for
and
. Thus, the DTFT can be obtained from
the DFT by simply replacing
by
, which corresponds
to infinite zero-padding in the time domain. Recall from
§7.2.10 that zero-padding in the time domain gives
ideal interpolation of the frequency-domain samples
(assuming the original DFT included all nonzero samples of
).